SOLUTION: alice can complete a project in 20 days and b0b can complete the same project in 30 days.alice and bob start working on the project together with alice quitting after some time ,an

Algebra ->  Rate-of-work-word-problems -> SOLUTION: alice can complete a project in 20 days and b0b can complete the same project in 30 days.alice and bob start working on the project together with alice quitting after some time ,an      Log On


   

Question 769503: alice can complete a project in 20 days and b0b can complete the same project in 30 days.alice and bob start working on the project together with alice quitting after some time ,and it takes bob another 10 days to complete the project.what is the total days to complete the project
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Alice can complete a project in 20 days 
So Alice's work rate is 1 project per 20 days or %281_project%29%2F20_days%29 or 1%2F20project%2Fday

and Bob can complete the same project in 30 days.
So Bob's work rate is 1 project per 30 days or %281_project%29%2F30_days%29 or 1%2F30project%2Fday

Their combined work rate is 1%2F20project%2Fday%22%22%2B%22%221%2F30project%2Fday = 1%2F20%2B1%2F30 = 3%2F60%2B2%2F60 = 5%2F60 = 1%2F12project%2Fday

alice and Bob start working on the project together with alice quitting after some time 
Suppose Alice quits after x days, 

then during those x days, together, at the rate of 1%2F12project%2Fday,
they finished x%2F12ths of the project.

it takes Bob another 10 days to complete the project.what is the total days to complete the project
Then during those 10 days, together, at the rate of 1%2F30project%2Fday,
Bob finished 10%2F30ths or 1%2F3rd of the project.

     The equation comes from:

      %22%22%2B%22%22 %22%22=%22%22%28matrix%283%2C1%2C1%2Ccomplete%2Cproject%29%29 

    x%2F12%22%22%2B%22%221%2F3 %22%22=%22%22 1

Multiply through by 12

     x + 4 = 12

         x = 8

Alice and Bob worked together for 8 days and Bob worked alone 10
days after that.

Answer: 8 + 10 = 18 days.

Edwin